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Multiple regression - goudprijs (EUR/kg)

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 23:40:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/25/t12275952738ej8p0xnzogczcp.htm/, Retrieved Tue, 25 Nov 2008 06:41:13 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/25/t12275952738ej8p0xnzogczcp.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10413.00 0.00 10709.00 0.00 10662.00 0.00 10570.00 0.00 10297.00 0.00 10635.00 0.00 10872.00 0.00 10296.00 0.00 10383.00 0.00 10431.00 0.00 10574.00 0.00 10653.00 0.00 10805.00 0.00 10872.00 0.00 10625.00 0.00 10407.00 0.00 10463.00 0.00 10556.00 0.00 10646.00 0.00 10702.00 0.00 11353.00 0.00 11346.00 0.00 11451.00 0.00 11964.00 0.00 12574.00 0.00 13031.00 0.00 13812.00 0.00 14544.00 0.00 14931.00 0.00 14886.00 0.00 16005.00 1.00 17064.00 1.00 15168.00 1.00 16050.00 1.00 15839.00 1.00 15137.00 1.00 14954.00 0.00 15648.00 1.00 15305.00 1.00 15579.00 1.00 16348.00 1.00 15928.00 1.00 16171.00 1.00 15937.00 1.00 15713.00 1.00 15594.00 1.00 15683.00 1.00 16438.00 1.00 17032.00 1.00 17696.00 1.00 17745.00 1.00 19394.00 1.00 20148.00 1.00 20108.00 1.00 18584.00 1.00 18441.00 1.00 18391.00 1.00 19178.00 1.00 18079.00 1.00 18483.00 1.00

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 11497.3225806452 + 5498.74638487208x[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	11497.3225806452	276.96417	41.5119	0	0
x	5498.74638487208	398.382466	13.8027	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.875564256511812
R-squared	0.766612767281083
Adjusted R-squared	0.762588849475584
F-TEST (value)	190.514022486624
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1542.07123720833
Sum Squared Residuals	137923054.636263

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	10413	11497.3225806452	-1084.32258064517
2	10709	11497.3225806452	-788.32258064516
3	10662	11497.3225806452	-835.322580645161
4	10570	11497.3225806452	-927.322580645161
5	10297	11497.3225806452	-1200.32258064516
6	10635	11497.3225806452	-862.322580645161
7	10872	11497.3225806452	-625.322580645161
8	10296	11497.3225806452	-1201.32258064516
9	10383	11497.3225806452	-1114.32258064516
10	10431	11497.3225806452	-1066.32258064516
11	10574	11497.3225806452	-923.322580645161
12	10653	11497.3225806452	-844.322580645161
13	10805	11497.3225806452	-692.322580645161
14	10872	11497.3225806452	-625.322580645161
15	10625	11497.3225806452	-872.322580645161
16	10407	11497.3225806452	-1090.32258064516
17	10463	11497.3225806452	-1034.32258064516
18	10556	11497.3225806452	-941.322580645161
19	10646	11497.3225806452	-851.322580645161
20	10702	11497.3225806452	-795.322580645161
21	11353	11497.3225806452	-144.322580645161
22	11346	11497.3225806452	-151.322580645161
23	11451	11497.3225806452	-46.322580645161
24	11964	11497.3225806452	466.677419354839
25	12574	11497.3225806452	1076.67741935484
26	13031	11497.3225806452	1533.67741935484
27	13812	11497.3225806452	2314.67741935484
28	14544	11497.3225806452	3046.67741935484
29	14931	11497.3225806452	3433.67741935484
30	14886	11497.3225806452	3388.67741935484
31	16005	16996.0689655172	-991.068965517241
32	17064	16996.0689655172	67.9310344827588
33	15168	16996.0689655172	-1828.06896551724
34	16050	16996.0689655172	-946.068965517241
35	15839	16996.0689655172	-1157.06896551724
36	15137	16996.0689655172	-1859.06896551724
37	14954	11497.3225806452	3456.67741935484
38	15648	16996.0689655172	-1348.06896551724
39	15305	16996.0689655172	-1691.06896551724
40	15579	16996.0689655172	-1417.06896551724
41	16348	16996.0689655172	-648.068965517241
42	15928	16996.0689655172	-1068.06896551724
43	16171	16996.0689655172	-825.068965517241
44	15937	16996.0689655172	-1059.06896551724
45	15713	16996.0689655172	-1283.06896551724
46	15594	16996.0689655172	-1402.06896551724
47	15683	16996.0689655172	-1313.06896551724
48	16438	16996.0689655172	-558.068965517241
49	17032	16996.0689655172	35.9310344827588
50	17696	16996.0689655172	699.931034482759
51	17745	16996.0689655172	748.931034482759
52	19394	16996.0689655172	2397.93103448276
53	20148	16996.0689655172	3151.93103448276
54	20108	16996.0689655172	3111.93103448276
55	18584	16996.0689655172	1587.93103448276
56	18441	16996.0689655172	1444.93103448276
57	18391	16996.0689655172	1394.93103448276
58	19178	16996.0689655172	2181.93103448276
59	18079	16996.0689655172	1082.93103448276
60	18483	16996.0689655172	1486.93103448276

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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